To answer this question we will use the following two points formula to compute the equation of a line that passes through two given points:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]
From the given table we get that the graph of the given linear function passes through (1,-5) and (2,-8) then its equation is:
[tex]y-(-5)=\frac{-8-(-5)}{2-1}(x-1).[/tex]
Simplifying the above result we get:
[tex]\begin{gathered} y+5=\frac{-8+5}{1}(x-1), \\ y+5=-3(x-1), \\ y+5=-3x+3. \end{gathered}[/tex]
Subtracting 5 from the above result we get:
[tex]\begin{gathered} y+5-5=-3x+3-5. \\ y=-3x-2. \end{gathered}[/tex]
Answer:
[tex]y=-3x-2.[/tex]
